ElsevierQuerol Vives, A.; Gallardo Bermell, S.; Ródenas Diago, J.; Verdú Martín, GJ. (2011). Parametric study of the X-ray primary spectra obtained with the MTSVD unfolding method. Applied Radiation and Isotopes. 69 (8)
1-INTRODUCTIONX-ray tubes used in radiodiagnostic range (10 -150 keV) require a complex Quality Control (QC)protocol. However, these QC procedures normally do not include any routine characterization of the primary photon beam. Normally, primary spectrum determination is skipped by measuring other QC parameters easier to be obtained in practice (high voltages, half value layer, homogeneity factor, ripple factor, etc).The use of direct spectrometry for determining primary X-ray spectrum is practically forbidden as detectors cease to work properly at high count rates. To avoid the pile-up effect in the detector produced The relation between the PHD and primary spectrum is defined by a Response function, expressed as a matrix. This Response matrix is ill conditioned and an unfolding method -such as MTSVD-should be applied to obtain the inverse matrix and hence the primary spectrum.It is necessary to qualify the accuracy of the unfolding method applied, to know whether the primary beam is properly reproduced.With this goal in mind, small variations in the working conditions are introduced to obtain different PHDs that after being unfolded are compared with reference spectra (IPEM 78 Report Catalogue).
THE MONTE CARLO MODELThe MC model developed includes a point source simulating the X-ray focus, the Compton spectrometer (Matscheko, 1998) and a Germanium detector (Canberra, 2009). A layout of the model can be seen in figure 1.The Compton spectrometer consists of a shielding chamber, a scattering chamber containing the scattering material (PMMA) and a spectrometer tube with lead collimators.The Compton scattering process produces an important decrease on the number of photons entering in the spectrometer tube. Therefore, statistics of the simulation is very poor. To improve statistics the geometry is splitted in two parts, as was presented in Gallardo et al., (2004). The final result, obtained with an F8tally, is the PHD in the detector.Electron transport has been activated in the model. However, a 10 keV energy cut-off has been applied to limit the total computer time.
THE RESPONSE FUNCTIONThe relation between PHD and the primary spectrum can be expressed by equation (1) Once R is known, the equation (1) (2). (2) Since R is a real MxN matrix, it admits a Singular Value Decomposition (SVD). But R is rank deficient, so there are many solutions for the Least Squares problem. An optimal solution can be obtained generating a new Response matrix and removing the parts of the solution corresponding to the smallest singular values (Golub and Van Loan, 1996).Then the MTSVD method can be used to obtain a new matrix, R k , where k is the number of singular values of R (or rank of R) that are considered (Forsythe et al., 1977).
RESULTS AND DISCUSSIONThree parameters of an X-ray tube have been tested: high volta...